Major props to Sandy55 for posting that tutorial on replacing the plastic rivets on an M. Be *very* careful if you go that route.
I gave it a try earlier with my m13, but I ended up bending the backplate too much during reassembly, so several keys were sticking or double registering due to imbalanced pressure on the membranes. I also wound up with a weird situation in that one of the replacement springs I ordered from Clickykeyboard was actually
defective: the spring was mounted on the hammer with the opposite orientation, so it wouldn't buckle properly! I didn't discover this until I had everything back and was reseating the keys... which meant that after all that hard work I still had a defective key!
I ended up buying another cheap M off Ebay and using the guts of that in my M13. It was an easy conversion, but I lost the trackpoint nub in the process. This is good, however, as I never liked it. I know I've desecrated a hideously rare keyboard, but I now have an excellent piece to code with at home and I don't ever intend to sell it
Also good timing as I just gave my dad my cherished '86 1390131 silver label M for Christmas and I was hoping to have the M13 ready for action before then. Turns out I got it working last night...heh. I'm gonna miss that keyboard... I'm not exaggerating when I say I've written well over a million lines of code on that board.
Edit:
Also, if you go that route you will have to convert the M13's 6 pin cable connector to a 4 pin one to get it working with the different board (you don't want a black keyboard with a grey cable, right?!). Let me know if you need the pinouts as I have them written down.